Apparatus and method to solve sudoku

ABSTRACT

An apparatus and method to solve sudoku. A gameboard contains a sudoku grid, with its rows, columns, and boxes identified, and means of mutually distinguishing its boxes. A group of tokens corresponding to each box is provided, along with means to associate each group of tokens within a unique box. Setup tokens are emplaced on the gameboard to mirror the setup identifiers of a sudoku puzzle to be solved. Then tokens are emplaced in home cells, straddling cells they could possibly wind up in, at or straddling heads or feet of rows or columns they may end up in, or off-board in queue waiting movement to a more defined position. A breakthrough board is disclosed wherein possible token positions may be erasably inscribed. A method to return the gameboard to pre-trial-and-error configuration using the breakthrough board is disclosed.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates mathematical puzzles, and in particular to an apparatus and method to solve sudoku.

2. Background of the Invention

Sudoku is thought to have originated in New York in the late 1970's, with Dell Magazines' publication of “number place” puzzles in its Puzzles and Logic Problems magazine. The game gained popularity in Japan during the 1980's, under the name Sudoku, which translates into ‘single number’. The puzzle has since become a world-wide phenomenon, with millions enjoying the solution of sudoku contained in numerous magazines and newspapers.

Referring now to FIG. 1, most sudoku puzzles consist of 9×9 grid 2, subdivided into nine 3×3 boxes 4, each of which box 4 contains nine cells 6, some of which contain setup identifiers, in this case setup numbers 12 (in some puzzles the setup identifiers, and units of play, may be letters, or any other appropriate unit). It may be noted that sudoku-like puzzles may incorporate different grid configurations, such as nine 2×3 boxes, sixteen 4×4 boxes, etc., and that any appropriate unit may be used, including numbers as described below, letters, etc.

One popular publisher designs sudoku using the rules that the setup number 12 pattern should be symmetrical (the pattern remains the same if you turn the puzzle upside-down), and no more than thirty setup numbers 12 are allowed. A well-designed sudoku puzzle has only one solution, and each step in arriving at that unique solution is normally based on logic, not guesswork, although a stymied player may resort to trial-and-error.

The object of the game is to fill in the empty cells 14 so that every row 8, column 10, and box 4 contains each of the numbers 1-9 only once.

A player is frequently able to fill in a number of empty cells 14 quickly, then is required to work at the next group of empty cells 14 and may get stuck until a breakthrough move is discovered, and then the final empty cells 14 may be completed quickly. Riding the wave of pleasant achievement accompanying the completion of the sudoku puzzle, the player may then be tempted to immediately start another, which syndrome has been credited with much of the addictive nature of the game.

A number of techniques are commonly used to solve sudoku. Scanning horizontal rows and vertical columns of boxes 4 may yield a unique location for one or more numbers, given that each box 4 may contain only a single exemplar of the numbers 1-9. For more complete descriptions of these and other sudoku solving techniques, see How to solve sudoku (Robin Wilson, The Infinite Ideas Company Limited, Oxford UK, 2005), hereby incorporated hereinto by reference.

Scanning rows 8 and columns 10 may yield a unique location for one or more numbers, given that each row 8 or column 10 may contain only a single exemplar of the numbers 1-9.

A player may inscribe candidate numbers 16 (also known as “little numbers”) in empty cells 14 representing possible number choices for each empty cell 14. This technique helps narrow the choices for empty cells 14, and may help determine correct numbers by elimination. Ultimately, if a player gets stalled, trial-and-error may be resorted to with an empty cell 14 which contains only two candidate numbers 16, which gives the player 50-50 odds of guessing correctly the first time.

A number of problems exist with the currently available sudoku game apparatus and methods. First, a common error made by sudoku players is to inscribe more than one of the same number in a given box 4. It would be desirable to eliminate the possibility of this error occurring.

A second problem with existing methods and apparatus is the inability to visualize which numbers remain to be filled into a given box 4. Players see the empty cells 14, but a clear visual reminder of which numbers should fill them may not be present. Accordingly, it would be desirable to provide clear visual reminders as to which numbers are available to fill empty cells 14.

A third problem is the frequently recurring situation where a player gets stalled, and is then unable to come up with the breakthrough move required to solve the puzzle. It would be advantageous to provide method and apparatus to isolate the numbers possible to fill the empty cells 14, so as to remove unnecessary clutter and facilitate focusing on the candidate numbers 16 which contain the key to the breakthrough move.

Still other problems exists where the trial-and-error sudoku solving technique is used. No clear apparatus and method to choose which trial to attempt first exists. And where a first attempt fails, no apparatus and method exists to return the sudoku board to the pre-trial configuration so as to attempt a different trial.

Existing Designs

A number of methods and apparatuses have been disclosed in an effort to facilitate the solution of sudoku puzzles. Morris 2008/0161106, Pechter 2007/0105077, and Terbush et al. 2007/0145681, 2008/0061504 all disclose apparatuses which subdivide, each cell into nine regions, one region for each number 1-9. The method taught involves marking regions or emplacing markers in regions, to specify which possible numbers may be inscribed in empty cells. While these devices avoided the hand-inscription of candidate numbers 16, they did require the laborious assignment of candidate numbers to cells. In addition, these apparatuses looked cluttered, and did not remove the candidate numbers from the sudoku board itself onto a clean breakthrough board to permit the player to consider a breakthrough move in an uncluttered environment.

Bohac 2007/0210516 disclosed an overlay upon which candidate numbers 16 could be inscribed. This apparatus suffered from the same disadvantages noted above.

Hunt 2008/0157469 taught a white-erase board upon which setup numbers 12, subsequently found numbers, and candidate numbers 16 could be erasably inscribed. While providing erasability, this apparatus did not solve the problem of avoiding cell double-entries, and resulted in the afore-mentioned clutter encumbering the previously mentioned art.

SUMMARY OF THE INVENTION

Accordingly, it is an object of the present invention to provide an apparatus and method to solve sudoku which improves a player's ability to visualize the numbers which have not yet been assigned a cell, and the possible cells these unassigned numbers can go into. Design features allowing this object to be accomplished include a color-coded gameboard, a plurality of color-code tokens, and a breakthrough board. Advantages associated with the accomplishment of this object include increased speed and satisfaction in playing sudoku.

It is another object of the present invention to provide an apparatus and method to solve sudoku which prevents number duplication within a box. Design features allowing this object to be accomplished include a color-coded gameboard, and a plurality of color-code tokens. Benefits associated with the accomplishment of this object include reduced playing errors, faster play, and increased player satisfaction.

It is still another object of this invention to provide an apparatus and method to solve sudoku which facilitates finding breakthrough moves. Apparatus features enabling the accomplishment of this object includes a dry-erase breakthrough board bearing a sudoku grid and a dry-erase marker. A method step enabling the accomplishment of this objective is inscribing candidate numbers from a sudoku grid to the breakthrough board grid. Advantages associated with the realization of this object include easier and faster identification of breakthrough moves, and increased speed of solving the puzzle and player satisfaction.

It is another object of the present invention to provide an apparatus and method to solve sudoku which facilitates trial-and-error puzzle solving. Apparatus features enabling the accomplishment of this object includes a dry-erase breakthrough board bearing a sudoku grid and a dry-erase marker. Method steps enabling the accomplishment of this objective include inscribing candidate numbers from a gameboard grid to the breakthrough board grid, and scrutinizing the inscribed breakthrough board for boxes containing a single cell with only two candidate numbers, or alternately two cells containing the same two candidate numbers (a duo, or twin). A benefit associated with the accomplishment of this object is faster and easier identification of trial-and-error attempt candidates.

It is still another object of this invention to provide an apparatus and method to solve sudoku which permits re-configuration of a sudoku gameboard grid back to pre-trial-and-error attempt status. Apparatus features enabling the accomplishment of this object includes an erasable breakthrough board bearing a sudoku grid and an erasable marker. Method steps enabling the accomplishment of this objective include inscribing candidate numbers from a sudoku grid to the breakthrough board grid, and referring to the breakthrough board grid candidate numbers to return the sudoku grid to pre-trial-and-error attempt status. Advantages associated with the realization of this object include faster and more accurate trial-and-error sudoku solving.

It is another object of the present invention to provide an apparatus and method to solve sudoku which facilitates puzzle solving. Apparatus features allowing this object to be accomplished include a color-coded gameboard, a plurality of color-code tokens. Method steps enabling the accomplishment of this objective include filling-the-boxes, scanning the grid, and scanning the rows and columns. Benefits associated with the accomplishment of this object include faster play, and increased player satisfaction.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention, together with the other objects, features, aspects and advantages thereof will be more clearly understood from the following in conjunction with the accompanying drawings.

Eight sheets of drawings are provided. Sheet one contains FIG. 1. Sheet two contains FIG. 2. Sheet three contains FIG. 3. Sheet four contains FIG. 4. Sheet five contains FIG. 5. Sheet six contains FIG. 6. Sheet seven contains FIG. 7. Sheet eight contains FIGS. 8-11.

FIG. 1 is a plan view of a prior art sudoku grid.

FIG. 2 is a plan view of a gameboard and the S tokens.

FIG. 3 is a plan view of a gameboard with setup tokens emplaced.

FIG. 4 is a plan view of a gameboard following the filling-the-boxes method step.

FIG. 5 is a plan view of a gameboard after the sudoku has been solved.

FIG. 6 is a plan view of a gameboard at a point where the player has gotten stalled.

FIG. 7 is a plan view of a breakthrough board annotated with the candidate numbers corresponding to the possible (unassigned) tokens depicted in FIG. 6.

FIG. 8 is a plan view of the R box of a gameboard with R tokens emplaced, just before a trial-and-error attempt is to be made.

FIG. 9 is a plan view of the top left box of a breakthrough board annotated with the candidate numbers corresponding to the unassigned tokens depicted in FIG. 8.

FIG. 10 is a plan view of the R box of a gameboard with R tokens emplaced, just after a failed trial-and-error attempt.

FIG. 11 is a plan view of the R box of a gameboard with R tokens returned to the positions they occupied immediately before a trial-and-error attempt depicted in FIG. 10 was made, by using the breakthrough board candidate numbers depicted in FIG. 9.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT Apparatus: Gameboard and Tokens.

FIG. 2 is a plan view of gameboard 20 and the tokens 30 associated with box S. Inscribed on gameboard 20 is the preferred embodiment sudoku grid 2, which is subdivided into nine 3-3 boxes 4, each of which box 4 contains nine cells 6. Thus, grid 2 comprises nine rows 8 and nine columns 10. Each row 8 is identified by an adjacent row identifier 9; each column 10 is identified by a column identifier 11. In the preferred embodiment row identifiers 9 were the capital letters A-I, and column identifiers 11 were the small case letters a-i.

Boxes 4 are identified via box identifiers 5. In the preferred embodiment, box identifiers from left to right were R, S and T for the top row of boxes 4; U, V, and W for the middle row of boxes 4; and X, Y and Z for the bottom row of boxes 4.

Boxes 4 incorporate means to distinguish each box 4 from the others, and means to associate a group of tokens 30 uniquely with each box 4. In the figures and description below, boxes 4 and groups of tokens 30 associated with each box 4 are identified by color, although it is intended to fall within the scope of this disclosure that any appropriate means of distinguishing each box 4 from the others, and means to associate a group of tokens 30 uniquely with each box 4, be used, including indicia, tactile textures, hatching, shading, etc.

In the preferred embodiment, box R was colored red (vertical solid line hatching), box S was colored green (diagonal solid line hatching), box T was colored blue (horizontal solid line hatching), box U was colored light blue (horizontal dashed line hatching), box V was colored purple (vertical dashed line hatching), box W was colored magenta (diagonal dashed line hatching), box X was colored pink (alternating vertical solid line and vertical dashed line hatching); box Y was colored yellow (horizontal/vertical cross-hatching), and box Z was colored orange (diagonal cross-hatching).

Each cell 6 contains a token home 44 to guide a player as to where to place a token 30 assigned to a cell 6 containing the token home 44. While FIG. 2 depicts token homes 44 as containing box color 46, it is contemplated that boxes 4 may be color-identified in any appropriate manner, including but not limited to token homes 44 containing box color 46, the entire box 4 being colored, the inside perimeter of each box 4 being shaded with a color hue, etc.

Rows of boxes are identified via box row identifiers 40. Columns of boxes are identified by box column identifiers 42. In the preferred embodiment, the box row identifiers 40 for the top, middle, and bottom rows of boxes were I, II and III respectively, and the box column identifiers 42 for the left, middle, and right rows of boxes were IV, V and VI respectively.

FIG. 2 also depicts the nine tokens 30 associated with box S. Each token 30 contains a token setup side 38 and a token playing side 39. When resting on a flat surface, either token setup side 38 or token playing side 39 faces upwards. In the preferred embodiment, tokens 30 were proportioned similarly to a dime.

Both token setup side 38 and token playing side 39 contain token color 34, which is the same color as the box 4 to which the token 30 is associated with. For example, all tokens 30 associated with box S are colored green, the same color as box S. Both token setup side 38 and token playing side 39 contain a token number 32. In the preferred embodiment, each box 4 had nine associated tokens 30 bearing token numbers 32 one through nine.

Although the figures depict the token 30 identifiers as being token numbers 32, it is intended to fall within the scope of this disclosure that token identifiers may be any appropriate unit, including letters, numbers, etc.

Each token setup side 38 bears a token ring 36 around its perimeter, to distinguish it from token playing side 39. When setting up tokens 30 on gameboard 20, one token 30 is emplaced, token setup side 38 (and token ring 36) up, in each gameboard 20 cell 6 corresponding to a cell 6 in a sudoku puzzle to be solved with contains a setup identifier, each token 30 thus emplaced has a token identifier same as the setup identifier in the corresponding cell in 6 the sudoku puzzle to be solved.

FIG. 3 is a plan view of a gameboard 20 with setup tokens 30 emplaced. Note that all tokens initially emplaced to set up gameboard 20 are placed with their token rings 36 visible, facing up. Once all the setup tokens 30 have been emplaced on grid 2, play may commence. Initially, all tokens on grid 2 are tokens bearing setup numbers 12, so identified by the fact that they are emplaced with their token setup sides 38 bearing token rings 36 facing up.

The height of each row 8 is substantially equal to the width of each column 10. Tokens 30 are sized such that a minimum of substantially one and a half tokens fits within the height of each row 8 or within the width of each column 10. In the preferred embodiment tokens 30 were disks, the height of each row 8 was substantially equal to the width of each column 10, and both were substantially equal to 1½ diameters of a token 30. Tokens 30 were all of the same size and proportionality.

Although the tokens 30 depicted in the drawings were circular, it is intended to fall within the scope of this disclosure that tokens 30 may be any shape, including but not limited to polygonal with any number of sides or irregularly shaped.

While the figures depict the popular 9×9 grid configuration containing nine 3×3 boxes, and the unit of play is numbers, it is intended to fall within the scope of this disclosure that the instant method be used with any grid configuration and unit. For example some two-dimensional sudoku-like games use different grid configurations, such as nine 2×3 boxes, sixteen 4×4 boxes, etc., and that other units may be used, including numbers as described above, letters, etc. The instant apparatus and method will also work effectively with these alternate embodiment two-dimensional matrix puzzles.

Sudoku Move Notation.

The following paragraphs describe a novel and convenient sudoku move notation system.

Cells are identified by the intersection of row and column, e.g. Ab (the cell defined by the intersection of row A and column b), Hd (the cell defined by the intersection of row H and column d), etc. As explained above, boxes are identified by their letter designation, e.g. R, S or W.

The following nomenclature is used to designate moves and terminology associated with sudoku play:

1-9 tokens—token setup side 38 facing up 1-9 tokens—token playing side 39 facing up AaAb either cell Aa or cell Ab AB either row A or B ab either column a or b (•) edge rows or columns M missing

N not

NG no good PT possible tokens Q queue ST stalled > move a token as pointed by the arrow, generally into rows, columns or boxes DUO two tokens fill up two cells in a row, column, or box (also known as a “twin” or “pair”) TRIO three tokens fill up three cells in a row, column, or box (also known as a “triplet”) QUAD four tokens fill up for cells in a row, column, or box (also known as a “quadruplet”) 3R the token bearing number 3 associated with box R (2)1 two possible 1s in a row or column RES necessary move to be able to resolve the puzzle 47 two possible tokens 4 and 7 in a cell

TOO The Only One Possible

TRY trial-and-error * breakthrough move

Method: Setup Gameboard Play.

This first step is the setup step. As explained previously in connection with FIG. 3, a plan view of a gameboard with setup tokens 30 emplaced, the first step of the instant method is to set up tokens 30 on gameboard 20. This is accomplished by emplacing one token 30, token setup side 38 up, in each gameboard cell 6 corresponding to a cell in a sudoku puzzle to be solved which contains a setup identifier (e.g. a setup number 12), each token 30 thus emplaced having a token identifier same as the setup identifier in the corresponding cell in the sudoku puzzle to be solved. Each setup token 30 thus emplaced should have a token color 34 same as the box color 46 in which it is emplaced. It pays to be careful in this step since an error could result in a duplicate digit in a row 8 or column 10.

The second step is the filling-the-boxes step. Referring now to FIG. 4 we observe a plan view of gameboard 20 following the filling-the-boxes method step. In this step, a player places all remaining tokens 30 on or around grid 2, token playing side 39 up. The simplest way to do this is to proceed box-by-box, in alphabetical order, using conventional sudoku techniques such as scanning horizontal and vertical rows of boxes 4 for unique locations for one or more numbers, given that each box 4 may contain only a single exemplar of the numbers 1-9, and scanning rows 8 and columns 10 to find unique locations for one or more numbers, given that each row 8 or column 10 may contain only a single exemplar of the numbers 1-9.

Where it can be determined (by elimination or otherwise) that a given token 30 can only go into one cell 6, such token is simply emplaced on (or assigned to) that cell 6. This situation is depicted in FIG. 4 by token 6W at cell Eg, and the play itself is annotated 6W>Eg (move the token 30 associated with box W bearing 6 as its token number 32 into cell Eg).

If a token 30 can be assigned to a unique cell it becomes an assigned token 30. If a token cannot be assigned to a unique cell 30, it is a possible token (abbreviated “PT”), and a player attempts to emplace it on or around grid 2 as described below, in descending order of preference.

Where it can be determined (by elimination or otherwise) that a possible token 30 can only go into two adjacent or tangential cells 6, that possible token 30 is emplaced straddling those two cells 6. This situation is depicted by token 3V at cells Ee, Ef in FIG. 4, and the play itself is annotated 3V>EeEf (move the token 30 associated with box V bearing 3 as its token number 32 to straddle cells Ee and Ef).

Where it can be determined (by elimination or otherwise) that a possible token 30 can only go into three adjacent cells 6 sharing a common corner, that possible token 30 is emplaced straddling those three cells 6. This situation is depicted by token 8S at cells Ad, Ae, Be in FIG. 4, and the play itself is annotated 8S>AdAeBe.

Where it can be determined (by elimination or otherwise) that a possible token 30 can only go into four adjacent cells 6 sharing a common corner, that possible token 30 is emplaced straddling those four cells 6.

Note that more than one possible token 6 may be emplaced at the same location. In this case, such possible tokens 30 may simply be stacked. This situation is depicted by possible tokens 3X, 4X and 6X at cells Gc, Hb, Hc in FIG. 4.

Where it can be determined (by elimination or otherwise) that a possible token 30 can only go into a single row 8, that possible token 30 is emplaced at the head or foot of that row 8. This situation is depicted in FIG. 8 by token 6R at the head of row A adjacent box R, and the play itself is annotated 6R>A.

Where it can be determined (by elimination or otherwise) that a possible token 30 can only go into a single column 10, that possible token 30 is emplaced at the head or foot of that column 10. This situation is depicted in FIG. 4 by token 5S at the head of column f adjacent box S, and the play itself is annotated 5S>f.

Where it can be determined (by elimination or otherwise) that a possible token 30 can only go into two rows 8, that possible token 30 is emplaced straddling the heads or feet of those two rows 8. This situation is depicted by token 2R at rows B and C adjacent box R in FIG. 4, and the play itself is annotated 2R>BC.

Where it can be determined (by elimination or otherwise) that a possible token 30 can only go into two columns 10, that possible token 30 is emplaced straddling the heads or feet of those two columns 10. This situation is depicted by token 9R at the heads of columns a and b adjacent box R in FIG. 4, and the play itself is annotated 9R>ab.

Note that more than one possible token 6 may be emplaced at the same location adjacent grid 2. In this case, such possible tokens 30 may simply be emplaced side-by-side, or head-to-toe. The head-to-toe situation is depicted by possible tokens 3R, 4R, 5R, 8R straddling the heads of columns b, c above box R in FIG. 4.

The important thing is that each possible token 30 be emplaced on an imaginary line extending perpendicularly away from a side of grid 2 (from a row 8, a column 10, or a point straddling same, as appropriate) so that a player can tell at a glance which row 8, column 10, or combination of two rows 8 or two columns 10, that the possible token 30 can go into.

Possible tokens 30 which cannot be emplaced as described above are left off gameboard 20 entirely, in queues adjacent their respective boxes. Queue tokens 30 associated with box V may be left off gameboard 20 off its upper left-hand corner, as depicted by 4W in FIG. 4. Other queue tokens 30 placed adjacent their respective boxes are depicted by tokens 7R, 1Y and 4Y in FIG. 4.

The following moves using the instant sudoku move notation take gameboard 2 from the setup configuration depicted in FIG. 3 to the “boxes-filled-in” configuration depicted in FIG. 4, proceeding box-by-box in ascending order:

Box R: 2R>BC, 3R>bc, 6R>AbAc, 7R>Q, 8R>bc, 9R>ab. Box S: 1S>AB, 2S>Cf, 5S>Cd, 7S>A, 8S>AdAeBe, 9S>AB. Box T: 1T>AhBgBh, 3T>gh, 4T>BgBh, 8T>Ci, 9T>gh. Box U: 2U>EF, 4U>bc, 5U>bc, 7U>DE, 8U>DbEbEc, 9U>DbEaEb. Box V: 1V>EF, 3V>EeEf, 4V>Q, 5V>f, 6V>EdEeFd, 8V>DdEdEe, 9V>DE. Box W: 1W>EF, 2W>EgEhFh, 4W>Q, 5W>h, 6W>Eg, 2W>EhFh, 1W>EhEiFh, 7W>DgDhEh. Row X: 3X>bc, 4X>bc, 5X>Ib, 3X>GcHbHc, 4X>GcHbHc, 6X>GcHbHc, 7X>Ga. Row Y: 1Y>Q, 3Y>ef, 4Y>Q, 6Y>GdHe, 7Y>I, 9Y>GH. Row Z: 1Z>Q, 2Z>Ig, 3Z>gh, 4Z>Q, 7Z>HgHh, 9Z>GgHgHh.

Once the filling-the-boxes step has been accomplished as described above (and as is depicted in FIG. 4), conventional sudoku techniques such as scanning the grid, scanning the boxes, scanning the rows and columns, filling the holes, finding unique home cells by elimination, unique resolution of ambiguity, etc., may be used to move the possible tokens 30 up the hierarchy of desirability explained above and into their home positions.

As play progresses, a player attempts to move possible tokens 30 up the hierarchy of desirability described above, into progressively more limited placement alternatives, until finally all possible tokens 30 are emplaced in respective unique cells, and become assigned tokens 30. When all possible tokens 30 have been assigned a unique cell 6, the sudoku puzzle has been solved. The solved sudoku puzzle is depicted in FIG. 5.

The following moves using the instant sudoku move notation take gameboard 2 from the “boxes-filled-in” configuration depicted in FIG. 4, to the puzzle solved configuration depicted in FIG. 5, first by scanning grid 2 for possible moves number-by-number, then using other techniques:

1: No moves.

2: 2R>Bc, 2U>Ea, 9U>DbEb, 7U>DbEbEc, 2W>Fh, 1W>EhEi.

3: No moves.

4: 4W>DE. 5: 5U>Fc, 5V>DfEf, 5W>DhEh, 4U>Fb, 4V>DE. 6: 6V>Fd, 6Y>He, 6X>Gc, 4X>Hc, 3X>Hb, 6R>Ab, 3R>c, 9R>Ca. 7: 7R>Cc, 3R>Ac, 8R>Bb, 3T>Cg, 7U>DbEb, 8U>Ec. 8: 8S>AdAe, 8V>Dd. 8S>Ae. 9: 9T>AhBgBh. Then: 1V>Ff, 1S>AdBe, 1Y>de.

9Y>G, 9Z>HgHh, 3Z>Ih, 1Z>G, 4Z>G, 1Y>IdIe, 3Y>Gf, 9Y>Gd, 5Y>I, 1Y>Ie, 1S>Ad, 7S>Af, 9S>Be, 7Y>Id, 4Y>If, 3V>Ee, 4V>Ed, 9V>DfEf, 9T>Ah, 1T>BgBh, 9Z>Hg, 7Z>Hh, 7W>Dg, 7U>Eb, 9U>Db, 9V>Ef, 5V>Df, 5W>Eh, 1W>Ei, 4W>Dh, 4T>Bg, 1T>Bh, 4Z>Gi, 1Z>Gg.

Being able to see the possible tokens 30, and to which cells 6 they are limited to be assigned, is a huge advantage in visualization compared to merely looking for number matches on a grid 2 otherwise blank except for the setup numbers 12 and those numbers which have been written into the grid by the player. It's analogous to playing bridge with a concise, easy-to-use list of all cards not in a player's hand, which haven't yet been played during the current game.

This advantage in visualization renders playing sudoku much easier, faster, and more satisfying to players, and can help a player solve a difficult sudoku puzzle which that player may otherwise be unable to solve.

Apparatus: Breakthrough Board.

If a player gets stalled (stuck), trial-and-error may be resorted to. This involves making a guess about which cell 6 a possible token 30 should be assigned to. It is preferable to make this guess using a possible token 30 which has only two possible cells into which it can go, which gives the player 50-50 odds of guessing correctly the first time. The instant breakthrough board 50 depicted in FIG. 7 facilitates identification of the best possible token(s) to use for trial-and-error attempt(s). In addition, where a trial-and-error attempt fails, breakthrough board 50 makes it possible to quickly and easily return gameboard 20 to the pre-trial-and-error configuration, ready for another trial-and-error attempt.

FIG. 6 is a plan view of a gameboard 20 at a point where the player has gotten stuck, or stalled. FIG. 7 is a plan view of a breakthrough board 50 annotated with the candidate numbers 16 corresponding to the possible tokens 30 depicted in FIG. 6.

Breakthrough board 50 is an erasable board comprising the following permanent markings: sudoku grid 2, row identifiers 9, column identifiers 11, box row identifiers 40, and box column identifiers 42. Marker 52 is used to erasably mark candidate numbers on breakthrough board 50. After a breakthrough move has been discovered, the erasable markings made on breakthrough board 50 may be quickly and easily erased. In the preferred embodiment, breakthrough board 50 was made of a white dry-erase material, and marker 52 was a dry-erase marker, whose marks on breakthrough board. 50 could be quickly and easily erased using a paper towel or dry cloth.

While the figures and the above description refer to an erasable marker 52, it is intended to fall within the scope of this disclosure that any apparatus capable of presenting an erasable breakthrough board be included, for example, a computer screen some of whose markings may be deleted, a slate with chalk, a mechanical screen erased by shaking, etc.

Method: Breakthrough Board Successful Trial-And-Error Attempt.

The first step in using breakthrough board 50 is to annotate breakthrough board 50 with the candidate numbers 16 corresponding to the possible tokens depicted in FIG. 6. This means that breakthrough board 50 will be annotated with all the possible numbers that must ultimately be assigned to breakthrough board 50 cells 6, and only with those numbers. The setup numbers are not transcribed to breakthrough board 50, nor are the numbers which have already been assigned to home cells. Only the unassigned candidate numbers 16 are annotated on breakthrough board 50.

This last point is extremely important. Only the unassigned candidate numbers are annotated on breakthrough board 50. No extraneous information unnecessary to the determination of the breakthrough move is written on breakthrough board 50. This is a big advantage to a player, because any such extraneous information unnecessary to the determination of the breakthrough move written on breakthrough board 50 would only clutter up breakthrough board 50, and make it more difficult for a player to discern the breakthrough move. Compare FIG. 1 to FIG. 7, imagining that all possible candidate numbers 16 had been inscribed on grid 2 in FIG. 1—a quantity of candidate numbers 16 of the same order as in FIG. 7. It's easy to tell at a glance that FIG. 7 provides the less cluttered presentation.

Candidate numbers 16 are annotated on breakthrough board 50 by simply writing the token number 32 of each possible token 30 in each cell such possible token 30 could go into. The easiest way to proceed is box by box, in ascending order. Let's consider box R.

Box R as depicted in FIG. 6 has four possible tokens: 3R, 5R, 7R and 9R. Token 3R can go into cells Ab or Cb (not Bb, because cell Bb is already assigned to token 8R). Therefore, the candidate number 3 is written in cells Ab, Cb. Token 5R can go into cells Aa or Ca (not Ba, because cell Ba is already assigned to token 6R). Therefore, the candidate number 5 is written in cells Aa, Ca.

Token 7R can go into cells Aa and Ab. Therefore, the candidate number 7 is written in cells Aa, Ab. Token 9R can go into cells Ca and Cb. Therefore, the candidate number 9 is written in cells Ca, Cb.

In this fashion, we have annotated the candidate numbers 16 corresponding to the possible tokens 30 in box R of gameboard 20, to the upper left box of breakthrough board 50. Proceeding in similar fashion with the remaining boxes S-Z, all candidate numbers 16 corresponding to the remaining possible tokens 30 depicted in FIG. 6 are annotated on breakthrough board 50. The result is FIG. 7.

Note that where a box 4 has associated possible token(s) 30 in queue, candidate numbers 16 pertaining to such queue possible token(s) are inscribed in each unassigned cell 6 in such box 4. For example, in box Z depicted in FIG. 6 there are two queue possible tokens: 1Z and 2Z. Regarding queue token 1Z, the candidate number 1 will be written in breakthrough board 50 cells Gg, Gh, Gi, Ih, and Ii. Regarding queue token 2Z, the candidate number 2 will be written in breakthrough board 50 cells Gg, Gi, and Ii (not in cells Gh and Ih, because a number 2 is already assigned to column h in cell Fh by setup token 2W).

Once breakthrough board 50 has been annotated with all candidate numbers 16 corresponding to the possible tokens 30 of gameboard 20, the breakthrough move may be determined in relative ease, aided by the uncluttered presentation of breakthrough board 50. In the situation depicted in FIG. 7, it becomes clear fairly readily that the TRIO 157 of cells Bh, Eh, Ih forces the breakthrough move 3T>Ah.

Therefore, the move 3T>Ah is played on gameboard 20, and the remainder of the solution of the sudoku puzzle depicted in FIG. 6 can proceed routinely. The candidate numbers 16 written on breakthrough board 50 can be quickly and easily erased, and breakthrough board 50 will be ready for the next time a player gets stalled.

Method: Breakthrough Board—Unsuccessful Trial-And-Error Attempt.

If a trial-and-error attempt has been made where the guess was incorrect, sooner or later it will become apparent that the guess was wrong. In that case, it is necessary to re-set gameboard 20 to the same configuration as immediately before the failed attempt. Breakthrough board 50 is very useful in this regard.

FIG. 8 is a plan view of the R box 4 of gameboard 20 with R tokens 30 emplaced, just before a trial-and-error attempt is to be made.

FIG. 9 is a plan view of the top left box 4 of a breakthrough board 50 annotated with the candidate numbers 16 corresponding to the possible tokens 30 depicted in FIG. 8.

FIG. 10 is a plan view of the R box 4 of gameboard 20 with R tokens 30 emplaced, just after a failed trial-and-error attempt.

FIG. 11 is a plan view of the R box 4 of gameboard 20 with R tokens 30 returned to the positions they occupied immediately before the trial-and-error attempt depicted in FIG. 10, by using the breakthrough board 50 candidate numbers 16 depicted in FIG. 9.

The method to re-configure gameboard 20 to the pre-attempt configuration includes the steps of removing each token 30 from a box 4 on gameboard 20 whose token number 32 equals a candidate number 16 in the corresponding breakthrough board 50 box 4; and of placing tokens 30 thus removed in possible token positions as explained in the filling-the-boxes step above.

In the example given, the box 4 is box R. The candidate numbers are 2, 3, 4, 5, 6, 8, 9. Therefore, token 2R>c, 3R>AbAc, 4R>C, 5R>ab, 6R>A, 8R>AcBc, and 9R>BC. Gameboard 20 is now reconfigured into the configuration it had immediately prior to the failed trial-and-error attempt, and is now ready for the next (hopefully successful) trial-and-error attempt.

In the preferred embodiment, gameboard 20, breakthrough board 50, and tokens 30 were made of plastic, metal, wood, synthetic, fiber board, or any other appropriate material. The face of breakthrough board 50 was dry-erase material, and marker 52 was a dry-erase marker. Tokens 30 where flat on token setup side 38 and playing side 39, and were chamfered around their outside edge to facilitate stacking them and turning them over.

While a preferred embodiment of the invention has been illustrated herein, it is to be understood that changes and variations may be made by those skilled in the art without departing from the spirit of the appending claims.

DRAWING ITEM INDEX

-   2 grid -   4 box -   5 box identifier -   6 cell -   8 row -   9 row identifier -   10 column -   11 column identifier -   12 setup number -   14 empty cell -   16 candidate numbers -   20 gameboard -   30 token -   32 token number -   34 token color -   36 token ring -   38 token setup side -   39 token playing side -   40 box row identifier -   42 box column identifier -   44 token home -   46 box color -   48 edge rows or columns (optional) -   50 breakthrough board -   52 marker 

1. An apparatus to solve sudoku comprising a gameboard and a plurality of tokens; said gameboard comprising: a plurality of horizontally disposed rows and vertically disposed columns organized into a grid; said grid comprising a plurality of boxes; each said box comprising a plurality of cells; means to distinguish each said box from other said boxes; said tokens being divided into groups, one said group of tokens corresponding to each said box, means to associate each said group of tokens with one said box, a number of tokens in each said group equaling a number of cells in a box with which said group of tokens is associated, each said token comprising a token identifier to distinguish said token from other said tokens in its group.
 2. The apparatus to solve sudoku of claim 1 wherein each said token comprises a token setup side and a token playing side, and means to distinguish between said token setup side and said token playing side.
 3. The apparatus to solve sudoku of claim 2 wherein a height of each said row is substantially equal to a width of each said column, and each said token is sized such that a minimum of substantially one and a half tokens fits within the height of each said row or within the width of each said column.
 4. The apparatus to solve sudoku of claim 2 wherein said gameboard further comprises means of identifying each said row and means of identifying each said column.
 5. The apparatus to solve sudoku of claim 2 wherein said gameboard further comprises means of identifying each said box.
 6. The apparatus to solve sudoku of claim 2 wherein said gameboard further comprises means of identifying each said row of boxes and means of identifying each said column of boxes.
 7. The apparatus to solve sudoku of claim 2 wherein said means to distinguish each said box from other said boxes is a color assigned to each said box, each said box being marked with a different color; and wherein said means to associate each said group of tokens with one said box is the color assigned to the box which said group of tokens is associated with, each said token within said group of tokens being marked with said color.
 8. The apparatus to solve sudoku of claim 7 wherein said token identifiers within a given group of tokens are ascending token numbers, the lowest said token number equaling 1 and the highest said token number equaling the number of cells in the box with which said given group of tokens is associated.
 9. The apparatus to solve sudoku of claim 4 wherein said means of identifying each said row comprises capital letters, and wherein said means of identifying each said column comprises small case letters.
 10. The apparatus to solve sudoku of claim 5 wherein said means of identifying each said box comprises capital letters.
 11. The apparatus to solve sudoku of claim 6 wherein said means of identifying each said row of boxes comprises Roman numerals, and wherein said means of identifying each said column of boxes comprises Roman numerals.
 12. The apparatus of claim 2 wherein said means to distinguish between said token setup side and said token playing side comprises a solid ring around an edge of each said token setup side.
 13. The apparatus to solve sudoku of claim 1 further comprising a breakthrough board and a marker, said breakthrough board comprising a breakthrough board grid permanently marked on it, a layout of said breakthrough board grid corresponding to a layout of the gameboard grid, said marker being an erasable marker whereby markings made by said marker on said breakthrough board are quickly and easily erased.
 14. The apparatus to solve sudoku of claim 13 further comprising, on said breakthrough board, means of identifying each said row and means of identifying each said column.
 15. The apparatus to solve sudoku of claim 14 further comprising, on said breakthrough board, means of identifying each said row of boxes and each said row of columns in said breakthrough board grid.
 16. The apparatus to solve sudoku of claim 1 further comprising a sudoku play nomenclature system comprising a row identifier identifying each row in said grid; a column identifier identifying each column in said grid; a means of identifying box/group identifier identifying each said box and its associated group of tokens; a token identifier identifying each token within each said group of tokens; and the conventions that each said cell is identified by its row identifier and its column identifier, each said token is identified by its token identifier and its box/group identifier, and that notation in the form xy>Jj means that a token of token identifier x of group y is moved to the cell located at an intersection of row J and column j.
 17. The apparatus to solve sudoku of claim 16 wherein said sudoku play nomenclature further comprises the conventions that xy>JjKk means that a token of token identifier x of group y is moved to a position straddling cells Jj and Kk, that xy>JjKkMm means that a token of token identifier x of group y is moved to a position straddling cells Jj, Kk and Mm, and that xy>JjKkMmNn means that a token of token identifier x of group y is moved to a position straddling cells Jj, Kk, Mm, and Nn.
 18. The apparatus to solve sudoku of claim 17 wherein said sudoku play nomenclature further comprises the conventions that xy>J means that a token of token identifier x of group y is moved to a head or foot of row J, that xy>j means that a token of token identifier x of group y is moved to a head or foot of column j, that xy>JK means that a token of token identifier x of group y is moved to a location straddling the head or foot of row J and a head or foot of row K, that xy>jk means that a token of token identifier x of group y is moved to a head or foot of column j and the head or foot of column k, and that xy>Q means that a token of token identifier x of group y is moved into a queue off the gameboard associated with group y.
 19. The apparatus to solve sudoku of claim 13 further comprising a sudoku play nomenclature system comprising a row identifier identifying each row in said breakthrough board grid; a column identifier identifying each column in said breakthrough board grid; a means of identifying each breakthrough board box; and the convention that each said breakthrough board cell is identified by its row identifier and its column identifier, and that notation in the form xy>Jj means that “x” should be erasably inscribed in breakthrough board cell Jj in breakthrough board box y.
 20. A method to solve a sudoku puzzle comprising the steps of: A. Providing a sudoku puzzle to be solved having setup identifiers in some of its cells; and an apparatus to solve sudoku comprising a gameboard and a plurality of tokens; said gameboard comprising: a plurality of horizontally disposed rows and vertically disposed columns organized into a grid; said grid comprising a plurality of boxes; each said box comprising a plurality of cells; means to distinguish each said box from other said boxes; said tokens being divided into groups, one said group of tokens corresponding to each said box, means to associate each said group of tokens with one said box, a number of tokens in each said group equaling a number of cells in a box with which said group of tokens is associated, each said token comprising a token identifier to distinguish said token from other said tokens in its group, a token setup side, and a token playing side, and means to distinguish between said token setup side and said token playing side; and B. Performing a setup step by emplacing one said token, setup side up, in each gameboard cell corresponding to a cell in said sudoku puzzle to be solved with contains a setup identifier, each said token thus emplaced having a token identifier same as the setup identifier in the corresponding cell in the sudoku puzzle to be solved, each token thus emplaced being emplaced in the box with which said token is associated.
 21. The method to solve a sudoku puzzle of claim 20 comprising the further filling-the-boxes steps of: C. Emplacing one said token playing side up in a gameboard cell in the box with which said token is associated if such cell is the only possible destination for said token in accordance with conventional sudoku rules. D. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into two adjacent or tangential gameboard cells in the box with which said token is associated, emplacing said token playing side up straddling said two adjacent or tangential gameboard cells; E. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into three adjacent gameboard cells sharing a common corner in the box with which said token is associated, emplacing said token playing side up straddling said three adjacent gameboard cells; and F. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into four adjacent cells sharing a common corner in the box with which said token is associated, emplacing said token playing side up straddling said four adjacent cells.
 22. The method to solve a sudoku puzzle of claim 21 comprising the further filling-the-boxes steps of: G. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into a single said row, emplacing said token playing side up at a head or foot of said row; H. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into a single said column, emplacing said token playing side up at a head or foot of said column; I. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into two said rows, emplacing said token playing side up straddling the heads or feet of said rows; J. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into two said columns, emplacing said token playing side up straddling the heads or feet of said columns; K. Where one said token cannot be emplaced as described above, emplacing said token in queue off said gameboard.
 23. The method to solve a sudoku puzzle of claim 22 comprising the further steps of: L. Providing a breakthrough board and an erasable marker, whereby marks made by said erasable marker are quickly and easily erased from said breakthrough board; M. Permanently printing on said breakthrough board a breakthrough board grid of a same layout as said gameboard grid; N. Erasably inscribing in the cells of said breakthrough board all the possible token identifiers which can go into said breakthrough board cells, determined in accordance with conventional sudoku rules; and O. Finding a breakthrough move in accordance with conventional sudoku rules by scrutinizing the inscribed breakthrough board.
 24. The method to solve a sudoku puzzle of claim 23 comprising the further step of erasing said possible token identifiers from said breakthrough board, whereby said breakthrough board is rendered ready to be used again.
 25. The method to solve a sudoku puzzle of claim 23 comprising the further steps of: P. Where no said breakthrough move can be found, scrutinizing said breakthrough board for a best cell with which to make a trial-and-error attempt; and Q. Making said trial-and-error attempt on said gameboard.
 26. The method to solve a sudoku puzzle of claim 25 comprising the further steps of: R. Where said trial-and-error attempt fails, removing from said gameboard the tokens bearing said possible token identifiers inscribed on said breakthrough board; and S. Emplacing said removed tokens on or around said gameboard as described in steps D through K above, whereby said gameboard is restored to a configuration same as prior to the failed trial-and-error attempt.
 27. An apparatus to solve sudoku comprising a gameboard and tokens, said gameboard comprising a 9×9 sudoku grid divided into nine 3×3 boxes of nine cells each and means of mutually distinguishing said boxes; said tokens being divided into nine groups of nine tokens each, and means of associating each said group of tokens with a unique said box.
 28. The apparatus to solve sudoku of claim 27 wherein each said token comprises a token setup side and a token playing side, and means to distinguish between said token setup side and said token playing side.
 29. The apparatus to solve sudoku of claim 28 wherein a height of each said row is substantially equal to a width of each said column, and each said token is sized such that at least one and a half tokens fits within the height of each said row or within the width of each said column.
 30. The apparatus to solve sudoku of claim 27 wherein said means of mutually distinguishing said boxes comprises a unique color in each said box, and wherein said means of associating each said group of tokens with a given said box comprises color on said group of tokens substantially the same as the color of the given said box with which said group of tokens is associated.
 31. The apparatus to solve sudoku of claim 30 further comprising a row identifier associated with each said row, a column identifier associated with each said column, and a box identifier associated with each said box.
 32. The apparatus to solve sudoku of claim 27 further comprising a breakthrough board permanently inscribed with a 9×9 sudoku grid divided into nine 3×3 boxes of nine cells each, and means of erasably writing on the breakthrough board grid.
 33. The apparatus to solve sudoku of claim 32 wherein said means of erasably writing on the breakthrough board grid comprises a dry-erase marker, and breakthrough board material suitable for inscription by a dry-erase marker.
 34. The apparatus to solve sudoku of claim 32 further comprising a row identifier associated with each said breakthrough board row, and a column identifier associated with each said breakthrough board column.
 35. A method to solve a sudoku puzzle comprising the steps of: A. Providing a sudoku puzzle to be solved; and an apparatus to solve sudoku comprising a gameboard and tokens, said gameboard comprising a 9×9 sudoku grid divided into nine rows, nine columns, nine 3×3 boxes of nine cells each, each said box bearing a unique color, a row identifier associated with each said row, a column identifier associated with each said column; said tokens being divided into nine groups of nine tokens each, a color on each said group of tokens substantially the same as the color of one said box with which such group of tokens is associated, the nine said tokens within each said group bearing a token number ranging between 1 and 9 respectively on a token setup side and a token playing side; and B. Performing a setup step by emplacing one said token, setup side up, in each gameboard cell which corresponds to a setup cell in said sudoku puzzle to be solved containing a setup number, each said token thus emplaced having a token number same as the setup number in the sudoku puzzle cell corresponding to the gameboard cell in which the setup token is emplaced.
 36. The method to solve a sudoku puzzle of claim 35 comprising the further steps of: C. When each said token is emplaced on said gameboard as described below, emplacing each said token with its playing side up; D. Emplacing one said token in a gameboard cell if such cell is the only possible destination for said token in accordance with conventional sudoku rules; E. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into two adjacent or tangential gameboard cells, emplacing said token straddling said two adjacent or tangential gameboard cells; F. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into three adjacent gameboard cells which share a common corner, emplacing said token straddling said three adjacent gameboard cells; G. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into four adjacent cells sharing a common corner, emplacing said token straddling said four adjacent cells; H. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into a single said row, emplacing said token at a head or foot of said row; I. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into a single said column, emplacing said token at a head or foot of said column; J. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into two said rows, emplacing said token straddling the heads or feet of said rows; K. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into two said columns, emplacing said token straddling the heads or feet of said columns; L. Where one said token cannot be emplaced as described above, emplacing said token off said gameboard in queue; M. Continuing to solve said sudoku puzzle in accordance with conventional sudoku rules, with each play moving said tokens as appropriate into home cells and into progressively more restricted positions on said gameboard, until all said tokens have been moved into respective cells, and said sudoku game is solved.
 37. The method to solve a sudoku puzzle of claim 36 comprising the further steps of: N. Providing a breakthrough board upon which numbers can be erasably written; O. Permanently printing on said breakthrough board a breakthrough board grid of the same layout as said gameboard grid; P. Erasably writing in corresponding cells of said breakthrough board all possible token numbers which can go into said gameboard board cells determined in accordance with conventional sudoku rules; and Q. Finding a breakthrough move in accordance with conventional sudoku rules by scrutinizing the inscribed breakthrough board.
 38. The method to solve a sudoku puzzle of claim 37 comprising the further step of erasing said possible token identifiers from said breakthrough board, whereby said breakthrough board is rendered ready to be used again.
 39. The method to solve a sudoku puzzle of claim 37 comprising the further steps of: R. Where no said breakthrough move can be found, scrutinizing said breakthrough board for a best cell with which to make a trial-and-error attempt; and S. Making said trial-and-error attempt on said gameboard.
 40. The method to solve a sudoku puzzle of claim 39 comprising the further steps of: T. Where said trial-and-error attempt fails, removing from said gameboard the tokens bearing said possible token identifiers inscribed on said breakthrough board; and U. Emplacing said removed tokens on or around said gameboard as described in steps C through L above, whereby said gameboard is restored to a configuration same as prior to the failed trial-and-error attempt.
 41. The method to solve a sudoku puzzle of claim 22 comprising the further steps of continuing to solve said sudoku puzzle in accordance with conventional sudoku rules, with each play moving said tokens as appropriate into home cells and into progressively more restricted positions on said gameboard, until all said tokens have been moved into respective cells, and said sudoku game is solved. 